title: Coarse-grained Monte Carlo simulations of non-equilibrium systems.
abstract: We extend the scope of a recent method for generating coarse-grained lattice Metropolis Monte Carlo simulations [X. Liu, W. D. Seider, and T. Sinno, Phys. Rev. E 86, 026708 (2012); and J. Chem. Phys. 138, 114104 (2013)] from continuous interaction potentials to non-equilibrium situations. The original method has been shown to satisfy detailed balance at the coarse scale and to provide a good representation of various equilibrium properties in both atomic and molecular systems. However, we show here that the original method is inconsistent with non-equilibrium trajectories generated by full-resolution Monte Carlo simulations, which, under certain conditions, have been shown to correspond to Langevin dynamics. The modified coarse-grained method is generated by simultaneously biasing the forward and backward transition probability for every possible move, thereby preserving the detailed balance of the original method. The resulting coarse-grained Monte Carlo simulations are shown to provide trajectories that are consistent with overdamped Langevin (Smoluchowski) dynamics using a sequence of simple non-equilibrium examples. We first consider the purely diffusional spreading of a Gaussian pulse of ideal-gas particles and then include an external potential to study the influence of drift. Finally, we validate the method using a more general situation in which the particles interact via a Lennard-Jones interparticle potential.
authors.affiliation: Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
authors.forename: Xiao
authors.initials: X
authors.lastname: Liu
authors.forename: John C
authors.initials: JC
authors.lastname: Crocker
authors.forename: Talid
authors.initials: T
authors.lastname: Sinno
mesh_terms: D004058:Diffusion; D056004:Molecular Dynamics Simulation; D009010:Monte Carlo Method